%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET637+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n019.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 14:39:41 EDT 2023

% Result   : Theorem 0.18s 0.56s
% Output   : Proof 0.18s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : SET637+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13  % Command    : do_cvc5 %s %d
% 0.12/0.33  % Computer : n019.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Sat Aug 26 14:28:13 EDT 2023
% 0.12/0.33  % CPUTime    : 
% 0.18/0.46  %----Proving TF0_NAR, FOF, or CNF
% 0.18/0.56  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.M8xpce4VqO/cvc5---1.0.5_8260.p...
% 0.18/0.56  ------- get file name : TPTP file name is SET637+3
% 0.18/0.56  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_8260.smt2...
% 0.18/0.56  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.18/0.56  % SZS status Theorem for SET637+3
% 0.18/0.56  % SZS output start Proof for SET637+3
% 0.18/0.56  (
% 0.18/0.56  (let ((_let_1 (forall ((B $$unsorted) (C $$unsorted)) (= (tptp.intersect B C) (tptp.not_equal (tptp.intersection B C) tptp.empty_set))))) (let ((_let_2 (not _let_1))) (let ((_let_3 (forall ((B $$unsorted)) (= (tptp.empty B) (forall ((C $$unsorted)) (not (tptp.member C B))))))) (let ((_let_4 (forall ((B $$unsorted) (C $$unsorted)) (= (tptp.not_equal B C) (not (= B C)))))) (let ((_let_5 (forall ((B $$unsorted) (C $$unsorted)) (= (= B C) (forall ((D $$unsorted)) (= (tptp.member D B) (tptp.member D C))))))) (let ((_let_6 (forall ((B $$unsorted)) (not (tptp.member B tptp.empty_set))))) (let ((_let_7 (forall ((B $$unsorted) (C $$unsorted)) (= (tptp.intersect B C) (exists ((D $$unsorted)) (and (tptp.member D B) (tptp.member D C))))))) (let ((_let_8 (forall ((B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.member D (tptp.intersection B C)) (and (tptp.member D B) (tptp.member D C)))))) (let ((_let_9 (tptp.empty tptp.empty_set))) (let ((_let_10 (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_11 (= tptp.empty_set _let_10))) (let ((_let_12 (tptp.empty _let_10))) (let ((_let_13 (forall ((C $$unsorted)) (not (tptp.member C tptp.empty_set))))) (let ((_let_14 (= _let_9 _let_13))) (let ((_let_15 (_let_3))) (let ((_let_16 (ASSUME :args _let_15))) (let ((_let_17 (_let_6))) (let ((_let_18 (ASSUME :args _let_17))) (let ((_let_19 (not _let_11))) (let ((_let_20 (tptp.not_equal _let_10 tptp.empty_set))) (let ((_let_21 (= _let_20 _let_19))) (let ((_let_22 (_let_4))) (let ((_let_23 (ASSUME :args _let_22))) (let ((_let_24 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_23 :args (_let_10 tptp.empty_set QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.not_equal B C)))) :args _let_22))) _let_23 :args (_let_21 false _let_4)))) (let ((_let_25 (tptp.intersect SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_26 (= _let_25 _let_20))) (let ((_let_27 (not _let_20))) (let ((_let_28 (forall ((D $$unsorted)) (or (not (tptp.member D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.member D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))))) (let ((_let_29 (not _let_28))) (let ((_let_30 (= _let_25 _let_29))) (let ((_let_31 (forall ((B $$unsorted) (C $$unsorted)) (= (tptp.intersect B C) (not (forall ((D $$unsorted)) (or (not (tptp.member D B)) (not (tptp.member D C))))))))) (let ((_let_32 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_33 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_32 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.intersect B C)))) :args (_let_31))) _let_32 :args (_let_30 false _let_31)))) (let ((_let_34 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_31 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_35 (not _let_34))) (let ((_let_36 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_31 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_37 (not _let_36))) (let ((_let_38 (or _let_37 _let_35))) (let ((_let_39 (forall ((D $$unsorted)) (= (tptp.member D tptp.empty_set) (tptp.member D (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))))) (let ((_let_40 (= _let_11 _let_39))) (let ((_let_41 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_31 _let_10))) (let ((_let_42 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_31 tptp.empty_set))) (let ((_let_43 (= _let_42 _let_41))) (let ((_let_44 (and _let_36 _let_34))) (let ((_let_45 (= _let_41 _let_44))) (let ((_let_46 (not _let_30))) (let ((_let_47 (_let_30))) (let ((_let_48 (_let_28))) (let ((_let_49 (not _let_26))) (let ((_let_50 (_let_2))) (let ((_let_51 (ASSUME :args _let_50))) (let ((_let_52 (or))) (let ((_let_53 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_51) :args _let_50)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_2) _let_1))) (REFL :args (_let_49)) :args _let_52)) _let_51 :args (_let_49 true _let_1)))) (let ((_let_54 (_let_26))) (let ((_let_55 (not _let_21))) (let ((_let_56 (_let_21))) (let ((_let_57 (_let_5))) (let ((_let_58 (ASSUME :args _let_57))) (let ((_let_59 (not _let_39))) (let ((_let_60 (_let_59))) (let ((_let_61 (_let_8))) (let ((_let_62 (ASSUME :args _let_61))) (let ((_let_63 ((tptp.member D (tptp.intersection B C))))) (let ((_let_64 (not _let_44))) (let ((_let_65 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_38)) :args ((or _let_35 _let_37 (not _let_38)))) (REORDERING (CNF_AND_POS :args (_let_44 1)) :args ((or _let_34 _let_64))) (REORDERING (CNF_AND_POS :args (_let_44 0)) :args ((or _let_36 _let_64))) (REORDERING (CNF_EQUIV_POS1 :args (_let_45)) :args ((or (not _let_41) _let_44 (not _let_45)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_31 QUANTIFIERS_INST_E_MATCHING _let_63)) :args _let_61)) _let_62 :args (_let_45 false _let_8)) (REORDERING (CNF_EQUIV_NEG1 :args (_let_43)) :args ((or _let_42 _let_41 _let_43))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_18 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_31 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member B tptp.empty_set) false))))) :args _let_17)) _let_18 :args ((not _let_42) false _let_6)) (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_60)) :args _let_60)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_59) _let_39))) (REFL :args ((not _let_43))) :args _let_52)) (REORDERING (CNF_EQUIV_POS2 :args (_let_40)) :args ((or _let_11 _let_59 (not _let_40)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_58 :args (tptp.empty_set _let_10 QUANTIFIERS_INST_ENUM)) :args _let_57)) _let_58 :args (_let_40 false _let_5)) (REORDERING (CNF_EQUIV_POS1 :args _let_56) :args ((or _let_27 _let_19 _let_55))) _let_24 (REORDERING (CNF_EQUIV_NEG1 :args _let_54) :args ((or _let_25 _let_20 _let_26))) _let_53 (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_48) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_31 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) false))))) :args _let_48)) (REORDERING (CNF_EQUIV_POS1 :args _let_47) :args ((or (not _let_25) _let_29 _let_46))) _let_33 :args (_let_29 false _let_34 false _let_36 false _let_44 false _let_45 false _let_41 true _let_42 true _let_43 true _let_39 false _let_40 true _let_11 false _let_21 false _let_20 true _let_26 false _let_38 true _let_25 false _let_30)))) (let ((_let_66 (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_28))))) (let ((_let_67 (forall ((C $$unsorted)) (not (tptp.member C (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))))) (let ((_let_68 (= _let_12 _let_67))) (let ((_let_69 (not _let_12))) (let ((_let_70 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_10))) (let ((_let_71 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_72 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_73 (and _let_72 _let_71))) (let ((_let_74 (= _let_70 _let_73))) (let ((_let_75 (not _let_71))) (let ((_let_76 (not _let_72))) (let ((_let_77 (or _let_76 _let_75))) (let ((_let_78 (not _let_77))) (let ((_let_79 (_let_29))) (let ((_let_80 (REFL :args (_let_77)))) (let ((_let_81 (_let_67))) (let ((_let_82 (and _let_11 _let_9))) (let ((_let_83 (ASSUME :args (_let_9)))) (let ((_let_84 (ASSUME :args (_let_11)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_82)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_83 _let_84) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM _let_84) :args (APPLY_UF tptp.empty)) (TRUE_INTRO _let_83))) :args (_let_9 _let_11))) :args (_let_11 _let_9))) :args (true _let_82)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_68)) :args ((or _let_67 _let_69 (not _let_68)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_81) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_ENUM)) :args _let_81)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_74)) :args ((or _let_70 (not _let_73) (not _let_74)))) (MACRO_RESOLUTION_TRUST (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_73)) :args ((or _let_76 _let_75 _let_73))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_77 1)) (CONG _let_80 (MACRO_SR_PRED_INTRO :args ((= (not _let_75) _let_71))) :args _let_52)) :args ((or _let_71 _let_77))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_77 0)) (CONG _let_80 (MACRO_SR_PRED_INTRO :args ((= (not _let_76) _let_72))) :args _let_52)) :args ((or _let_72 _let_77))) :args ((or _let_77 _let_73) false _let_71 false _let_72)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_79)) :args _let_79)) (CONG _let_66 (REFL :args (_let_78)) :args _let_52)) _let_65 :args (_let_78 true _let_28)) :args (_let_73 true _let_77)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING _let_63)) :args _let_61)) _let_62 :args (_let_74 false _let_8)) :args (_let_70 false _let_73 false _let_74)) :args ((not _let_67) false _let_70)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_16 :args (_let_10 QUANTIFIERS_INST_ENUM)) :args _let_15)) _let_16 :args (_let_68 false _let_3)) :args (_let_69 true _let_67 false _let_68)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args _let_56) (CONG (REFL :args (_let_55)) (REFL :args (_let_20)) (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_11))) :args _let_52)) :args ((or _let_20 _let_11 _let_55))) (MACRO_RESOLUTION_TRUST (CNF_EQUIV_NEG2 :args _let_54) _let_53 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args _let_47) (CONG (REFL :args (_let_46)) (REFL :args (_let_25)) _let_66 :args _let_52)) :args ((or _let_25 _let_28 _let_46))) _let_65 _let_33 :args (_let_25 true _let_28 false _let_30)) :args (_let_27 true _let_26 false _let_25)) _let_24 :args (_let_11 true _let_20 false _let_21)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_14)) :args ((or _let_9 (not _let_13) (not _let_14)))) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_6 (= B C)))) _let_18 :args (_let_13 false _let_6)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_16 :args (tptp.empty_set QUANTIFIERS_INST_ENUM)) :args _let_15)) _let_16 :args (_let_14 false _let_3)) :args (_let_9 false _let_13 false _let_14)) :args (false true _let_12 false _let_11 false _let_9)) :args (_let_8 _let_7 _let_6 _let_5 _let_4 (forall ((B $$unsorted) (C $$unsorted)) (= (tptp.intersection B C) (tptp.intersection C B))) (forall ((B $$unsorted) (C $$unsorted)) (=> (tptp.intersect B C) (tptp.intersect C B))) _let_3 _let_2 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.18/0.57  )
% 0.18/0.57  % SZS output end Proof for SET637+3
% 0.18/0.57  % cvc5---1.0.5 exiting
% 0.18/0.57  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------